A non-obvious arithmetical property of the binomial triangle becomes apparent from these balanced ternary lists: the rows which have an odd prime number as an index and only these rows are represented by a ternary list where 1 and -1 are alternating. One might also say that an odd integer is prime iff n > 1 and its binomial notation is zerofree.

Finally a(n) = sum_{0<=k<n} T(n)[k]*3^k.

The sequence starts at n=0 although the definitions can be extended to the negative integers by flipping the signs of the ternary digits. To illustrate the definitions: